For the spread: place the cream cheese, goat cheese, garlic, thyme, parsley, 5 tablespoons milk, salt, and pepper in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed until well-mixed. Add an additional tablespoon of milk if the spread is very thick.

To make the sandwiches: spread each slice of the bread with the goat cheese spread. Slice the cucumber into thin rounds and arrange on half of the bread slices. Top with the remaining bread and press slightly. Cut the sandwiches into halves, thirds, or triangles.